Running Head: ANALYTIC READING SKILLS INSTRUCTION AND MATHEMATICAL PROBLEM SOLVING 1 The Effects of Explicit Analytic Reading Skills Instruction on the Ability to Solve Mathematical Problems in a Written Format in a Third-Grade Classroom Megan Long University of Arkansas T.G. Smith Elementary
SOLVING 2 Abstract This study was designed to determine if explicit analytic reading skills instruction used in a third-grade classroom would improve mathematical problem solving. The analytic reading skills instruction consisted of teaching students to analytically read a mathematics problem in order to find the purpose, organize the information, draw conclusions and then begin to plan and implement solutions in order to accurately solve the problem. The intervention for this study consisted of direct teaching and independent practice work four days a week, for eight weeks focusing each day on analytic reading strategies and applying those to mathematical word problems. The intervention was conducted for 50 minutes each day. The students were assessed daily using a scoring rubric. These scores were then compared to the pre-test and post-test scores of the mathematical problem solving assessment, reading, and mathematics tests. Based on the results of the assessments, the mathematical problem solving abilities of the students improved because of explicit analytic reading skills instruction.
SOLVING 3 TABLE OF CONTENTS ABSRACT.. 2 LIST OF TABLES.. 7 LIST OF FIGURES. 8 CHAPTER I. INTRODUCTION... Background of the Problem.... Definition of Terms..... 9 9 10 11 Purpose and Significance of the Study... II. REVIEW OF LITERATURE... Mathematical Word Problem Solving. 13 14 Issues Related to Solving Math Problems in a Written Format: Textbooks and Instruction... 15 Issues Related to math Problems in a Written Format: Reading Skills of Students. Teaching Reading in Mathematics... 16 17 Recommendations for Explicit Analytic Reading Skills Instruction... 18 Explicit Analytic Reading Skills of Mathematical Word Problems..... Summary.... III. METHODOLOGY..... District Setting.... 19 20 21 21
SOLVING 4 School Setting... Participants... Confidentiality... Data Collection... Evaluation Instrument... Baseline Data... Other Data Collection Methods... Post Data Analysis... Intervention Strategies... Summary... IV. RESULTS............ Baseline Data... During Intervention... Post Intervention... Data Analysis... Subpopulations... Male and Female... 22 23 24 25 25 28 28 29 29 31 32 32 36 37 41 42 42 English Language Learners and Non-English Language Learners... Anecdotal Records... Summary... 43 43 46 43 V. DISCUSSION......... Conclusions Limitations... 47 49 51
SOLVING 5 Implications... Recommendations... Summary... 52 53 54 REFERENCES............ 55 APPENDICES A IRB Approval Form... 57 B School Approval Letter... 58 C Parent Letter... 59 D Informed Consent... 61 E ACTAAP Assessment... 64 F Mathematics Reading Test... 83 G Mathematics Computation Test... 85 H Analytic Scoring Scale... 87 I J Scope and Sequence of Instruction Day 1 Lesson Plan... 88 89 K Student Work... 90 L Day 2 Lesson Plan... 91 M Student Work... 92 N Day 3 Lesson Plan... 93 O Day 4 Lesson Plan... 94 P Student Work... 95 Q Mathematics Problem Solving Pre-Test Scores 97 R Analytic Reading Skills Pre-Test Scores.. 98 S Mathematical Computation Skills Pre-Test Scores.. 99 T Sample of Individual Student Scores. 100
SOLVING 6 U Mathematical Problem Solving Post-Test Scores... 101 V Mathematical Computation Skills Post-Test Scores 102 W Analytic Reading Skills Post-Test Results. 103 X Mathematical Problem Solving t-test Results... 104 Y Individual Mathematical Problem Solving Gender Results 105 Z Gender Mathematical Problem Solving t-test Results 106 AA Individual ELL and Non-ELL Results... 107 BB ELL and Non-ELL Mathematical Problem Solving t-test Results 108 CC Anecdotal Record Table 109
SOLVING 7 List of Tables Table 1. Table 2. Results Obtained from t-test for Mathematical Problem Solving.. Results Obtained from t-test for Gender. 42 43
SOLVING 8 List of Figures Figure 1 District Demographics... 22 Figure 2 School Demographics... 23 Figure 3 Participants Demographics... 24 Figure 4 Percentage of students achievement categories in mathematical problem solving... 34 Figure 5 Percentage of students achievement categories in mathematical computation skills... 35 Figure 6 Percentage of students in each analytic reading skills achievement category... 36 Figure 7 The class mean of weekly averages for mathematics word problem solving... 37 Figure 8 Inidividual student written format problem solving scores... 38 Figure 9 Percentage of students achievement categories in mathematical problem solving... 38 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Individual student mathematical computation skills... Student achievement scores based on computation skills.. Individual student analytic reading skills scores Student achievement scores based on analytic reading skills. Pre- and post-intervention scores of ELL and non-ell students 39 40 40 41 43
SOLVING 9 Chapter I Introduction The current emphasis on mathematics instruction and the recent implementation of the Common Core State Standards Initiative calling for college and career ready students, requires the ability to read mathematics problems in a written format, then find an accurate solution to that problem (Common Core State Standards Initiative [CCSSI], 2011). Adams (2003) asserts that many students struggle to solve mathematical word problems because they have trouble reading, comprehending and understanding the language of the problem. Additionally, literature (Fuchs, Fuchs, Compton, Powell, Seethaler, Capizzi & Schatschneider, 2006; Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp & Jacek, 2003) proposes that children struggle to solve mathematical word story problems because the problems are complex and hard for them to grasp. Numerous experts (Griffin & Jitendra, 2008; Jitendra, Griffin, Deatline-Buchman & Sczeniak, 2007; Jitendra, Griffin, Haria, Leh, Adams & Kaduvettor, 2007) indicate that traditional textbook problem solving instruction lacks effectiveness in improving students abilities to solve mathematical problems in a written format; and many teachers do not provide varied instruction required for them to improve the ability to fluently solve these problems. Other literature (Barton, Heidema, Jordan, 2002; Vilenius-Tuohimaa, Aunola, & Nurmi, 2008) suggests that explicit analytic reading skills instruction improves students ability to solve mathematical problems in a written format. Background of the Problem The National Center for Education Statistics (NCES) (2011) found that many students struggle to achieve basic proficiency in mathematics and reading. They also assert that reading and mathematics are the foundations to success later in school. Adams (2003) proclaims that
SOLVING 10 students are not fluently and accurately solving mathematical problems in a written format due to the lack of understanding of the specific language, and not comprehending the written text. He also adds that students do not consider mathematical written text a language; and therefore, do not utilize reading strategies in order to understand the text. Furthermore, Jitendra et al. (2007) and Griffin and Jitendra (2008) suggest that students are not properly instructed to solve mathematical word problems. They further assert that teachers rely on the use of textbooks for instruction, which do not effectively teach children to reason and make connections. These experts opine that this hinders students ability to effectively solve written format mathematical problems. Definition of Terms To facilitate the understanding of this research report, the following terms are defined: 1. Arithmetic skills are defined as the ability to solve math problems that involve whole numbers, fractions, decimals, and percent using solving methods such as addition, subtraction, multiplication and division (Griffin & Jitendra, 2008). 2. Computation is defined as determining an amount or number of a problem using different operations and strategies, such as addition, subtraction, multiplication, and division (Griffin & Jitendra, 2008). 3. Conceptual model word problem diagram is a way to organize story grammar and information and express mathematical relations in word problems (Xin, Wiles, & Lin, 2008). 4. Explicit analytic reading skills instruction is teaching students specific reading strategies that will help them to understand the language and meaning of the text that is written (Barton, Heidema, Jordan, 2002; Vilenius-Tuohimaa, Aunola, & Nurmi,
SOLVING 11 2008). It has been operationalized for this study to mean an active process that teaches students to analyze a problem, mentally organize information, make decisions based on the text, and bring thoughts and opinions to what they read. 5. Mathematical problems in a written format mean problems that involve printed language of a mathematical problem. (Fuchs, Fuchs, Compton, Powell, Seethaler, Capizzi & Schatschneider, 2006; Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp & Jacek, 2003). This term has been operationalized for this study to mean mathematical problems that are text based and not just numeral based. 6. Semantic structure is defined as making connections of meanings, understandings, and relationships to mathematical operations (Griffin & Jitendra, 2008). 7. Visual-spatial displays means mentally constructing information in a variety of ways in order to organize information (Xin, Wiles, & Lin, 2008). Purpose and Significance of the Study The purpose of this study was to investigate the effects of explicit analytic reading skills instruction on the ability to solve mathematical problems in a written format in one third-grade classroom. The intent was to determine if teaching students how to read analytically to analyze a problem, organize information based on the purpose and the text, make decisions, and engage critically with what they read improves the ability to translate narrative format mathematic problems into numeric operations and then accurately solve the problem. Because explicit analytic reading skills instruction seems to improve students ability to comprehend and solve math problems in a written format successfully, teachers may use these strategies in order to improve students abilities to understand and solve mathematical word problems. This study looked at the effects of explicit analytic reading skills instruction on mathematical problems in a
SOLVING 12 written format in third graders, and the research question was, Does explicit analytic reading skills instruction improve student s ability to solve mathematical problems in a written format in one group of third-grade students? This research report is organized into five chapters. Chapter I offered a statement of introduction for this study, which was conducted to determine the effects of analytic reading skills instruction on the ability to solve mathematical problems in a written format in third-grade students. Chapter II provides a review of literature concerning mathematical problems in a written format and explicit analytic reading skills instruction. Chapter III serves to explain the methodology for this study. The setting, participants, data collection, procedures, instruments, and analysis are shared. Chapter IV serves to explain the results of this study. Baseline data, during intervention and post intervention analysis are shared. Chapter V draws conclusions and implications, then makes recommendations based on the results of the study are shared.
SOLVING 13 Chapter II Review of Literature This chapter provides a comprehensive, yet not exhaustive, review of literature on mathematical word problems and analytic reading skills instruction. The intent of this chapter is to review relevant research and other literature that supports the argument that teaching students how to analyze a problem, organize information based on the purpose and the text, make decisions, and engage critically with what they read improves the ability to translate narrative format mathematic problems into numeric operations and then accurately solve them. Literature (Fuchs, Fuchs, Compton, Powell, Seethaler, Capizzi & Schatschneider, 2006; Fuchs, Fuchs, Prentice, Burch, Hamlett, Owen, Hosp & Jacek, 2003) suggests that children are struggling to solve mathematical word story problems because of the complexity of the solution process. Additionally, literature (Griffin & Jitendra, 2008; Jitendra, Griffin, Deatline-Buchman & Sczeniak, 2007; Jitendra, Griffin, Haria, Leh, Adams & Kaduvettor, 2007) indicates that traditional textbook problem solving instruction is not effective in improving students abilities to solve mathematical problems in a written format. Teachers must provide several different varieties of instruction for students to learn to solve these problems. Adams (2003) suggests that many students who struggle with solving mathematical word problems have trouble reading, comprehending, and understanding the language of the problem. Other literature (Barton, Heidema, Jordan, 2002; Vilenius-Tuohimaa, Aunola, & Nurmi, 2008) suggests that using explicit analytic reading skills instruction improves students ability to solve mathematical problems that are in a written format. This chapter is organized so that literature on mathematic word problem solving and the importance is reviewed first, and then literature detailing issues related to mathematic word
SOLVING 14 problem solving is discussed. Studies and expert opinion on teaching reading in mathematics is presented, followed by recommendations for teacher instruction to implement these practices in the classroom. Finally, support is given for using analytic reading instruction to improve students ability to solve mathematical problems in a written format. Mathematical Word Problem Solving Research (Jitendra et al., 2007; Griffin & Jitendra, 2008) asserts that story problems present difficulties for many students. These experts say solving these problems poses difficulties because they require students to understand the language and factual information of the problem, and translate the problem with pertinent information to create an acceptable mental representation. The students must then devise and monitor a solution plan, and implement effective technical computations. According to Griffin and Jitendra learning how to solve story problems involves knowledge about semantic structure and mathematical relations. They emphasize the notion that students need to know basic arithmetical skills and strategies in order to solve problems in a written format. Jitendra et al. describe story word problems as critical in helping children make connections of meanings, understandings, and relationships to mathematical operations. A source (National Council of Teachers of Mathematics [NCTM], 2011) emphasizes that problem solving is an essential part of the k-12 mathematics curriculum. The authors emphasize the importance of integrating mathematical word problem solving strategies and skills. They assert that mathematical word problems can promote students conceptual understanding, foster their ability to reason and communicate mathematically, and capture their interests and curiosity. The authors further declare that developing students abilities to solve problems is not only a fundamental part of mathematics learning across content areas but also an integral part of mathematics learning across grade levels.
SOLVING 15 Issues Related to Solving Math Problems in a Written Format: Textbooks and Instruction in the Classroom Research (Jitendra et al., 2007; Griffin & Jitendra, 2008) suggests that many math textbooks do not provide sufficient instruction on reasoning and making connections to help students solve story problems. These researchers point out that many textbooks are organized so each problem is solved by the same procedure therefore hindering students ability to distinguish among problems that require different solving methods. These authors further declare that teaching students to look for key words is misleading. They proclaim that this method does not assist students in problem solving because it does not address the meaning and structure of the problem and therefore does not improve reasoning and deciphering solutions. Furthermore, they believe the teachers must scaffold and offer instructional facilitation during the learning process. These authors agree that many classrooms lack in this type of instruction. They go on to proclaim that teachers lack of depicting problems visually and graphically and their failure to use explicit instruction and interactions between peers delays student s ability to solve word problems. In order for students to comprehend solving problems in a written format that teaching instruction must be done using a variety of methods. Griffin and Jitendra (2008) suggest that providing problem solving and opportunities, emphasizing mathematical thinking and reasoning, are essential for students to problem solve effectively. Fuchs et al. (2003) studied eighty-eight 3 rd grade students and their teachers to determine if clearly teaching for transfer by using several different strategies improved students abilities to solve word problems. These strategies included promoting a higher level of abstraction, and increasing metacognition in mathematical problem solving. They found that
SOLVING 16 strong instruction designed to teach rules for problem solution is important in the classroom and will help students to solve story problems efficiently. Issues Related to Solving Math Problems in a Written Format: Reading Skills of Students Several sources (Adams, 2003; Ponce & Garrison, 2005; Velinius-Tuohimaa, Aunola, Nurmi, 2008) identify many issues related to student s difficulties solving written mathematical problems. Velinius-Tuohimaa et al. (2008) studied 225 children aged 9-10 to investigate the relationship between mathematical word problem skills and reading comprehension skills. Students expository and narrative reading comprehension counting skills were tested. Based on the results, math performance and reading skills are very closely related, and math problem solving performance and comprehension reading skills were correlated to overall reasoning skills. This study suggests there are specific skills needed for students to process written information, such as decoding skills and reading comprehension. It further suggests that these play a role in understanding the overall problem and helps being able to effectively solve the problem. The authors affirm that technical reading level and reading comprehension contribute to students performance in solving written math problems. Ponce and Garrison (2005) stress the notion that if a student does not have the understanding of what a problem is saying they are not able to figure out the meaning. The authors posit that for these students this becomes an issue of comprehension, and frustrates students because they are not able to effectively solve written format problems. Adams (2003) urges educators to emphasize the notion that mathematics is a language and not just something that we do: He reminds us that ignoring this means children may miss the concepts of mathematics that enhance and reinforce their understanding. He asserts that the words, terminology and vocabulary used in mathematics are critical factors in comprehending
SOLVING 17 and communicating answers to problems, and that recognizing and employing formal definitions is essential to understanding and applying important mathematical concepts when reading text. Adams emphasizes the importance of teaching mathematics as a language. He asserts that teachers have to provide different reading strategies in order for students to comprehend mathematical problems in a written format. Teaching Reading in Mathematics Sources (Barton, Heidema & Jordan, 2002; Gyamfi, Bossé, & Faulconer, 2010) recommend teaching specific reading skills to improve the ability to solve mathematical story problems. They state that the skills that are needed for reading math text are different or may not have been used in other content areas, and thus teaching these specific reading strategies improves student s ability to solve mathematical word problems. Barton et al. (2002) state that learning to read mathematics is essential in understanding the meaning of the problem and being able to implement a solution effectively. He further suggests that by using specific reading strategies that this is the best way to help students make sense and learn from the mathematical text read. They also express the notion that teachers can incorporate reading and learning strategies that will help activate prior knowledge, master vocabulary, and make sense of unfamiliar text. Similarly, Gyamfi et al. (2010) suggest that reading serves as a means for extracting or receiving mathematical understanding. These authors claim that purposefully directed classroom assessments and instruction are a necessity in order for students to read to learn mathematics. The suggestions of the authors are that teachers include problems that require them to reflect on the ideas, formulating definitions, reading, and expressing those ideas in writing in order to communicate their thinking. Gyamfi et al. note that teaching children reading strategies that will help them analyze, understand the problem, form definitions and express their
SOLVING 18 own thoughts and ideas are essential to them solving mathematical problems that are in a written format. Recommendations for Explicit Analytic Reading Skills Instruction The components behind using explicit analytic reading skills instruction are teaching reading strategies that will have children analyze a problem, mentally organize information, make decisions based on the text, and bring thoughts and opinions to what they read. Experts (Barton et al., 2002; Ediger, 2002; Gersten, Jordan & Flojo, 2005) recommend teaching reading skills through targeted interventions in order to help students to accurately solve written mathematical problems. Barton offers several recommendations for teaching children who struggle with the reading of a mathematical problem. She suggests the teachers activate prior knowledge because this prepares students to make meaningful connections, draw conclusions and assimilate new ideas. She claims this helps them better learn from and remember what they have read. Barton also notes the importance of mathematical vocabulary and text style. She says teaching vocabulary instruction should include maps, webs and other graphic organizers to assist students in relating familiar topics to construct visual representations which aid in understanding. Barton also proclaims that in order for learners to be able to make sense of text style, instruction should be based on finding the main idea of the problem and ignoring all of the irrelevant information. Another method that she suggests can be used by a teacher is to conduct a think aloud on a passage of text that has confusing units, and by modeling how to identify the main ideas and make logical inferences this will aid in the students making reason of the text style. Xin, Wiles, and Lin, (2008) studied five students grades 4 and 5 who were at risk for mathematical disabilities and concluded that teachers should focus on textual analysis of story and analyze the problem mapping key elements of the problem and connecting those elements to
SOLVING 19 past understanding. The researchers suggest that educators use a conceptual model diagram to prompt the learner to identify different elements in word story problems, and lay out a visualspatial display for representing those key elements. Xin, Wiles, and Lin (2008) assert that using this method will aid in the understanding of the main ideas and grammar of the word problems. They proclaim that using this method will help in the solving process. Explicit Analytic Reading Skills of Mathematical Word Problems Many respected researchers, (Barton et al., 2002; Gyamfi et al., 2010; Xin et al., 2008) support the notion that using explicit analytic reading skills instruction in elementary school classrooms can improve the ability to solve mathematical problems that are in a written format. Barton (2002) pronounced that teachers should incorporate different reading and learning techniques to help students draw inferences, understand vocabulary, and illicit meaning from the text. For that reason, other experts (Ediger, 2002; Vilenius et al., 2008) posit that the academic of solving word problems will improve when classroom instruction includes specific reading strategies. Similarly, Ediger (2002) asserts that adopting and implementing explicit analytic reading skills instruction helps the learners build a stronger foundation and understanding of how to solve written mathematical problems. They propose that these practices aid in reading and analyzing the problem, organizing information, understanding specific vocabulary, and formulating answers and opinions, to apply to the solution. Adams (2003) asserts that regarding mathematics as a language enhances and reinforces understanding of problems. Barton agrees that if children understand the language of mathematical word problems, and if teachers supplement instruction to build those reading strategies, then students performance on solving written mathematical problems will improve.
SOLVING 20 Summary Based on literature (Adams, 2003; Fuchs et al., 2006; Griffin & Jitendra, 2008) that point to the notion that students struggle with solving mathematical problems that are in a written format due to reading, lack of instruction and misleading textbook information, and other experts (Barton et al., 2002; Gyamfi et al., 2010; Vilenius-Tuohimaa et al., 2008) who claim that using explicit analytic reading skills instruction will improve children s ability to solve mathematical word problems, it appeared that a study examining the impact of explicit analytic reading instruction on mathematical problems in a written format was necessary. The next chapter details the methodology of the study.
SOLVING 21 Chapter III Methodology This study investigated the effects of explicit reading skills instruction on the ability to solve mathematical problems of a written format in a third-grade classroom. It was intended to determine if teaching students how to analyze a problem, organize information based on the purpose and the text, make decisions, and engage critically with what they read improves the ability to translate narrative format mathematic problems into numeric operations and then accurately solve the problem. This chapter describes the setting, the participants, and the confidentiality procedures for this study. How data were collected and the evaluation instruments are also described. The intervention strategy is explained and the methods for analyzing the data are detailed. District Setting This study took place at an elementary school in Northwest Arkansas. Demographic information for the school district provided in this section is based on the published information from the 2011-2012 school year (Arkansas Department of Education [ADE], 2012). The school district serves students from pre-kindergarten through grade 12. The district in which the school is located has a total number of 19,376 students in 25 schools, which is an increase in the student population from the 2010-2011 school years of 5.66%. There are 9,428 elementary students, 2,908 middle-school students, 2,763 junior-high students, and 3,711 high-school students. The ethnic breakdown for the school district is as follows: 8,137 White: 356 Asian: 438 Black: 8,359 Hispanic: 94 American Indian; and 1,701 Pacific Islanders (see Figure 1). There are 1,787 students involved in the district s special education program, and 8,279 students classified as Limited-English-Proficient in the district.
SOLVING 22 8.91% 2.29% 42.63% 1.86% 1.52% 0.49% 43.79% Hispanic White Pacific Islander Black Asian Two or More Races Native American Figure 1. Racial demographics for the school district in Northwest Arkansas. School Setting The elementary school in this study has a total population of 608 students (ADE, 2012). The student population consists of 264 White students, 250 Hispanic students, 55 Pacific Islander students, 14 Black students, 10 Asian students, and 11 American Indian students (see Figure 2). According to the 2011-2012 District Profile (ADE, 2011), this elementary school had 414 students on free/reduced lunch, which was 68% of the student population. This school houses a hearing-impaired classroom and serves 10 students with hearing impairments. All 10 of the students who are primarily served in this classroom are also included in the appropriate general education classrooms for some portion of each day with necessary provisions and supports. There are 7 faculty members who are part of the special education faculty at this school. Additionally, this elementary school is one of a selected few in the district to implement the Toyota Family Literacy Program, which is a literacy initiative funded in part by Toyota that focuses on increasing literacy among Hispanic families. As a part of this program, interested Hispanic parents attend a class held four mornings per week with lessons and instruction
SOLVING 23 designed to increase their own literacy and English skills while also learning how to help their children improve while at home. There are 6 Literacy and ESL specialists employed by this elementary school that work with the students in this school alongside this program. 9.04% 1.64% 2.30% 1.80% 0.65% White 43.42% Hispanic Pacific Islander 41.11% Black Asian Native American 2 or More Races Figure 2. Racial demographics for the elementary school in Northwest Arkansas. Participants This study was conducted in a third-grade general education classroom consisting of 24 students. There are 13 females and 11 males in the classroom. The racial demographics of the students in this classroom are as follows: 12 Hispanic students, 10 White students, 1 Asian/Pacific Islander, and 1 Black student. 19 of these students receive free lunches at school, and 2 receive reduced lunches. There are 12 English Language Learner students in the classroom at varying levels. One student is in the Gifted and Talented program that student goes to the GT room once a week. Additionally, one student receives a variety of special education services. This student goes to the resource room for an hour and a half daily during reading and writing instruction to get supplemental instruction.
SOLVING 24 4% 4% 42% 50% Hispanic White Asian Black Figure 3: Racial demographics for the elementary school in Northwest Arkansas. Confidentiality Permission to conduct the study was granted by the University of Arkansas Institutional Review Board (see Appendix A), as well as the administration of the elementary school where the study was conducted (see Appendix B). Permission to participate in this study was obtained prior to the commencement of the project. A letter (see Appendix C), along with an Informed Consent (see Appendix D), was sent home with each student in the appropriate language, and a signature from the parent or guardian was required before data for that child were reported. The informed consent explained the purpose and procedures of the study. It explained that participating is completely voluntary and that there is no reward or penalty for participating. It explained that the child may withdraw from the study at any time without penalty. Confidentiality will be maintained and assured by the researcher through the establishment of a code. Each student was assigned by the researcher through the establishment of a code. Each student was assigned a number at random to establish the code. All data were recorded anonymously using the code. Only the researcher had access to the code, and all data were kept
SOLVING 25 in a locked file cabinet in the project classroom. After this study is defended, the code will be destroyed. Data Collection This study was designed to examine the effects of explicit analytic reading skills instruction on the ability to solve mathematical problems in a written form of one group of thirdgrade students. Data were collected to determine if reading skills instruction structured around teaching students how to read analytically to analyze a problem, organize information based on the purpose and the text, make decisions, and engage critically with what they read improves the ability to translate narrative format mathematic problems into numeric operations and then accurately solve the problem. During the nine week intervention period, the ability to solve mathematical problems in a written format was determined through scores that are recorded daily and weekly and anecdotal records. Evaluation instruments. In order to get complete understandings of math problem solving skills, ability to read and understand the test, and compute mathematical operations were measured. Three different tools were used to establish skills and abilities to solve mathematical problems before and after the intervention. Released items from the Arkansas Comprehensive Testing, Assessment and Accountability Program (ACTAPP) (see Appendix E for a sample of the assessment) and a researcher developed reading test and a mathematics skills test were used. A fourth tool was used during intervention, a six point analytic scoring scale used to determine students ability to solve mathematical problems during the study. ACTAAP. The ACTAPP is a comprehensive system encompassing high academic standards, professional development, student assessment, and accountability for schools. The focus of ACTAAP is to measure student learning and classroom instruction; provide
SOLVING 26 accountability by establishing expected achievement levels and reporting on student achievement; provide program evaluation data; and assist policymakers in the decision-making process. The released items from the math section measure students ability to solve mathematical problems in a written format. The problems require students to read, analyze, choose a computation method and compute a solution effectively. Scores on the open response section are calculated using a scoring tool that focuses on the students ability to state the correct answer, a correct and completed procedure is shown, or the answer is explained. Scores range from 4, being the highest, to 1, being the lowest. There are 4 points are possible on each problem, 2 points are awarded if each part has the correct answer. Also 2 points are awarded if correct and completed procedure are shown and/or explained of how the response was determined. A response may earn one half of a point if the procedure contains a counting or copy error or is incomplete. A response that meets each of these criteria earns 4 points. A score of 3 is awarded if it earns 3-3 ½ points, a score of 2 is awarded if it earns 2-2 ½ points are earned; and a score of 1 was awarded if it earns ½-1 ½ points. In the multiple-choice section one point is awarded for each correct answer. That is translated into a percentage in order to gain understanding of the abilities of mathematical problem solving. The test is timed and administered to the entire group at one setting. The testing lasts approximately 40 minutes each time it is administered. The scores are calculated according to the rubric described above, and individual participant scores are recorded in the examiner record book. Each student s ability to solve mathematical problems is noted. The written format problem solving scores were classified using the baseline data into three achievement categories: advanced, proficient, and basic. In order to compare end results with baseline data, each of these categories were given a specific range of scores that did not
SOLVING 27 change when the end results were analyzed. These ranges were formulated based on the ranges of pretest scores. Scores of 60 and above were classified as advanced; scores between 59 and 31 were classified as proficient; scores of 30 and below were classified as basic. There was 1 advanced, 14 proficient, and 9 basic. Researcher developed reading test. This researcher developed analytic reading test was administered in order to gain an understanding of students ability to read and analyze of a story problem. This multiple choice test was developed using some of the questions from the ACTAAP. The questions provide a mathematical story problem which requires the students to read the problem and answer what the story is about by choosing the correct multiple choice answer. This test measured students abilities to read a mathematical story problem and be able to analyze it in order to answer what the main idea of the story is (see Appendix F for sample assessment). The test is not timed and is administered to the entire group at one setting. The scores were calculated by dividing the number of correct responses by the number of questions and converting it into a percentage. The individual participant scores were recorded in the examiner record book to not each student s reading abilities. Researcher developed mathematical computation skills test. A mathematical computation skills test was administered to gain an understanding of students abilities to solve mathematical computations. This test was developed using the ACTAAP test for assessing students mathematical problem solving skills. The test requires the students to solve mathematical exercises that were already set up in the form of number aligned with operation symbols provided (see Appendix G for sample assessment).
SOLVING 28 The test is not timed and administered to the entire group at one setting. The scores are calculated by dividing the number of correct responses by the number of questions and converting it into a percentage. The individual participant scores are recorded in the examiner record book and each student s mathematical computation skills are noted. Analytic scoring scale. This scale measured students ability to analyze a problem, plan a solution, and compute an answer. The scoring tool has three section; understanding the problem, planning a solution, and getting the answer. Scores range from 6 to 0 with 6 being the highest and 0 being the lowest. Each section has two points possible. The students were asked to learn the different strategies such as analyzing a problem, mentally organizing information, making decisions based on the text, and bringing thoughts and opinions to what they read (see Appendix H for scoring scale). Baseline data. In order to establish a baseline for students abilities to solve problems in a written format, released items from the ACTAAP was administered on December 14, 2011. A researcher developed mathematics and reading tests was administered on December 15, 2011. The students scores from these tests served to establish the levels of abilities to solve math word problems, and read mathematics problems prior to the implementation of explicit reading skills instruction. Other data collection methods. Data were collected during the intervention period to monitor and record students progress related to solving mathematical word problems. Data were collected in the form of daily and weekly scores, as well as by recording observed anecdotes related to solving word problems. Daily scores were recorded as students are taught different reading strategies that aid in solving mathematical word problems. Students were scored using an Analytic Scoring Scale. The students were given a story problem that they analyzed, answered
SOLVING 29 questions, and found solutions to show understanding of the problem. At the end of each week, students mathematical word problem solving abilities were assessed by computing daily scores into weekly averages. Data that were recorded daily and weekly were organized and analyzed to determine results throughout this study. Post data analysis. In order to determine the effectiveness of explicit analytic reading skills instruction on the ability to solve mathematical problems in a written format, released mathematics items from the ACTAAP and two researcher developed mathematics skills and reading tests were re-administered to each student following the same method as utilized before. The post-assessment results were examined and compared to the baseline data. A paired-samples t-test was conducted to determine if a significant difference exists between the pre-test and posttest scores. Data were collected by recording daily and weekly scores and by recording anecdotal records. Anecdotal records were coded and analyzed to determine patterns and themes which may appear. Daily and weekly records, along with pre-test and post-test assessments, and anecdotal records were carefully examined and analyzed to determine changes and trends, and then conclusions were drawn. Intervention Strategies During the course of this study students learned to implement analytic reading skills to precisely and accurately read and comprehend mathematical text and compute an accurate solution. The specific strategies taught were intended to help students analyze a problem, mentally organize information, make decisions based on the text, and bring thoughts and opinions to what they read. The intervention instruction lasted fifty minutes, 4 days per week, for 9 weeks. Students were taught one of the four strategies each day for the first week of the study, beginning with analytically analyzing a problem and ending with bringing thoughts and opinions
SOLVING 30 to what they read. The strategies were to analyze a problem, mentally organize information, make decisions based on the text and bring thought and opinions to what they read. The study took place Monday through Thursday of each week during a fifty minute period. Each week followed the same patterns of instruction with a different analytic reading strategy being the focus each day and different mathematical skills and word problem type taught each week (see Appendix I for intervention schedule). The same sequence of instruction followed each week. Day 1. The analytical reading strategy that would be taught that day such as finding the main idea of the word problem was introduced as a whole explicit group instruction. Along with the reading strategy, the mathematics concept for that day was introduced by using explicit whole group instruction. The students were provided with information and data in a written format which they read and analyzed the problem then applied the reading strategy that was learned (see Appendix H for sample lesson plan and Appendix I for student work). Day 2. The reading strategy and mathematical concept from the previous day was reviewed as a whole group instruction. A new analytic reading strategy was introduced, such as finding the supporting details and mathematics concept using direct instruction and moving onto guided practice. The final is independent practice where the students were provided with a type of mathematical problem that included the mathematics concept learned that day (see Appendix J for sample lesson plan and Appendix K for student work) Day 3. The reading strategy and mathematical concept from the previous two days were reviewed as a whole group instruction. A new analytic reading strategy and a mathematics concept was then introduced using explicit direct whole group instruction. The students then applied the information learned from the previous two days in order to correctly find the main idea, and supporting details and then begin to use those to plan and explain a solution. The
SOLVING 31 students were then provided with independent work that allowed them to apply the reading strategies learned previously and accurately plan and explain a solution (see Appendix L for sample lesson plan). Day 4. The mathematical and reading concepts from the previous three days were reviewed as a whole group instruction. Guided practice was then used to model how to apply the concepts and reading strategies in order to solve mathematical problems in a written format. The students applied all of the mathematical concept knowledge and reading strategies that were previously learned and put it all together in order to accurately solve mathematics word problems. The students were provided with mathematical problems in a written format in which they were to independently put all of the reading strategies together in order to plan, explain, and find an accurate solution (see Appendix M for sample lesson plan and Appendix N1 and N2 for student work). Summary The CCSSI calls for ensuring all students are college and career ready. They also raise concerns about the current state of mathematics in our school. In order for students to understand mathematical problems in a written format they must first comprehend the language and the text, and be able to effectively implement a solution to the problem. It is suggested that explicit analytic reading skills instruction improves student ability to solve mathematical problems in a written format. This study was intended to examine the effects of explicit analytic reading skills instruction on the ability to solve mathematical problems in a written format. This study was conducted in an elementary school in Northwest Arkansas for a 9-week with obtained approval.
SOLVING 32 Chapter IV Results The purpose of this chapter is to provide analyses of data collected for the study designed to address the research question, Does explicit analytic reading skills instruction improve the ability to solve mathematical problems of a written format in one group of third-grade students? Data are presented through narrative text and supported with tables and figures. The purpose of this study was to determine if teaching students how to analyze a problem, organize information based on the purpose and the text, make decisions, and engage critically with what they read improves the ability to translate narrative format mathematic problems into numeric operations and then accurately solve the problem. Twenty-five students from a local elementary school participated in the study. Over the course of nine weeks, students participated in daily mathematical word problem activities. The ability to solve mathematical problems in a written format was determined by the ability to analytically read the problem in order to find the purpose, organize and eliminate information that is not needed, plan and explain a solution, and accurately compute the solution to the mathematics word problem. Daily and weekly scores for solving mathematical word problems were gathered and recorded during the study using explicit analytic reading skills instruction. Baseline Data Baseline data were established by calculating problem solving accuracy on the ACTAPP released items, and 2 researcher developed instruments. The pre-assessment scores for the ACTAAP were obtained during the week of December 12, 2011 and the 2 researcher developed test scores were obtained on December 14 and 15, 2011. The ACTAPP scoring tool focuses on the students ability to state the correct answer, show a correct and completed procedure, and
SOLVING 33 explain the answer of a mathematical problem in a written format. The baseline scores were established by dividing the number of correct responses by the total number of responses; resulting in a percentage. Additionally the analytic reading skill and mathematical computation skills scores were measured by recording as a percent of accuracy. These scores were collected before the commencement of the study to establish baseline word problem solving abilities prior to explicit mathematics instruction focused on using analytic reading skills. Baseline scores were recorded for problem solving skills, analytic reading skills and mathematics computation skills prior to explicit mathematics instruction focused on using analytic reading skills. Mathematical problem solving. Students ability in solving mathematical problems of a written format was measured using ACTAAP. The highest possible ability average was 100, and the lowest possible average was 0. The maximum-recorded score was 62 and the minimumrecorded score was 17. The range was 45. The mean score was 37. The median score was 34. The mode was 31 (see Appendix Q for individual student scores). There was one score that was identified as an outlier because it was greater than 1.5 times the Inter-Quartile Range above the Upper Quartile value and was not included in this t-test. The mathematical problem solving scores were classified using the baseline data into three achievement categories: advanced, proficient, and basic. In order to compare end results with baseline data, each of these categories were given a specific range of scores that did not change when the end results were analyzed. These ranges were formulated based on the ranges of pretest scores. Scores of 60 and above were classified as advanced; scores between 59 and 31 were classified as proficient; scores of 30 and below were classified as basic. There was 0 advanced, 21 proficient, and 3 basic. Figure 4 illustrates the percentage of students who scored in each achievement category.
SOLVING 34 12% 4% 84% Proficient Basic Advanced Figure 4. Percentage of students achievement categories in mathematical problem solving. Mathematical computation skills. Students ability in responding to mathematical computation skills was also measured using a researcher developed test from mathematical problems on the ACTAAP. The ability to solve computations was determined by taking the number of problems worked correctly and dividing it by the total number of problems. These scores were recorded as percentages. Thus, the highest possible accuracy score was 100 and the lowest 0. The maximum-recorded was 82 and the minimum-recorded was 36. Thus, the range was 45. The mean score was 67. The median was 73. The mode was 82 (see Appendix R for individual student scores). There were no scores that were identified as outliers. The scores were classified using the baseline data into three achievement categories: advanced, proficient, and basic. In order to compare end results with baseline data, each of these categories were given a specific range of scores that did not change when the end results were analyzed. These ranges were formulated based on the ranges of pretest scores. Scores of 90 and above were classified as proficient; scores between 89 and 60 were classified as proficient; and scores of 59 and below were classified as basic. There was 0 scores classified as advanced, 18 scores classified as proficient, and 6 scores classified as basic. Figure 5 illustrates the percentage of students who scored in each achievement category.
SOLVING 35 0% 25% 75% Proficient Basic Advanced Figure 5. Percentage of students achievement categories in mathematical computation skills. Analytic reading skills. Students analytic reading skills were determined by scoring the ability to comprehend just the text of the mathematical word problems by taking the number of problems worked correctly, and dividing it by the total number of problems. Scores were established in accuracy percentages. Thus, the highest possible score was 100 and the lowest was 0. The maximum-recorded analytic reading skills score was 100 and the minimum-recorded was 17. Thus, the range was 83. The mean score was 47. The median score was 50. The mode was 33 (see Appendix S for individual student scores). There were four scores that were identified as outliers because 3 were 1.5 times the Inter-Quartile Range above the Upper Quartile value and 1 were 1.5 times the Inter-Quartile Range below the Lower Quartile value. The analytic reading skills scores were classified using the baseline data into three achievement categories: advanced, proficient, and basic. In order to compare end results with the baseline data, each of these categories were given a specific range of scores that did not change when the end results were analyzed. These ranges were formulated based on the ranges of pretest scores. Scores of 70 and above were classified as advanced; scores between 69 and 30 were classified as proficient; and of 30 and below were classified as basic. There were 3 scores